What is the value of $c o t (- 315 °)$ ?

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Solution

Find the value of $\cot (- 315 °)$ .
$\begin{array}{rcl} \cot (- 315 °) & = & - \cot 315 ° \{∵ \cot (- θ) = - \cot (θ)\} \\ \Rightarrow & \cot (- 315 °) = - \cot (360 ° - 45 °) {∵ \cot (360 ° - θ) = \cot (θ)} \\ \Rightarrow & \cot (- 315 °) = - \cot (45 °) \\ \Rightarrow & \cot (- 315 °) = - 1 \{Put \cot (45 °) = - 1\} \end{array}$
Hence, the value of $\begin{array}{l} \cot (- 315 °) \end{array}$ is $- 1$ .

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